equation find m and n

Question

If m^2 + n^2 = 140 and mn=49, what is the vaule of (m-n)^2?

 

a. 0

b. 24

c. 238

d. 42

Answer 1

Solve for m² from the first equation.

 

m² = 140 - n²

 

 

Square both sides of the second equation.

 

m²n² = 2401

 

 

Substituting the first equation into the shorter equation,

 

n²(140 - n²) = 2401

 

-n⁴ + 140n² = 2401

 

0 = n⁴ - 140n² + 2401

 

 

Let     q = n²

 

0 = q² - 140q + 2401

 

 

Use the quadratic formula to solve for q.   Then

 

n = ±√q

 

 

Plug in this value of n into the first equation to solve for m.  Under these conditions,

 

m and n are both positive or both negative.

 

 

Once you have both m and n, you can find (m-n)².

 

Answer 2

(m-n)²=m²-2mn+n²=140-2(49)=140-98=42

You only asked for m-n. The question title asks for more.